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Course 447: Applied Kalman Filtering with Emphasis on GPS-Aided Systems

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Course 447: Applied Kalman Filtering with Emphasis on GPS-Aided Systems

Instructor: Mr. Michael Vaujin, Consultant
2.4 CEUs
Onsite onlyOur most requested courses are offered at different public venues two to three times per year. Most of our courses also can be taught onsite at your location. Most on-site courses can be customized to your needs. Read more about our on-site course options.

Course Description

This is a highly intensive 4-day short course on Kalman filtering theory and Kalman filtering applications. Included is a discussion of linear, extended, unscented, and square root Kalman filters and their practical applications to real-time strapdown navigation and target tracking. Exposure to Information filters, 2nd and 3rd order extended Kalman filters, particle filters, integrity monitoring, and methods of smoothing is included. Emphasis is on practical applications, but sufficient supporting theory is provided for further research. Designed for engineers who need a working knowledge of Kalman filtering or who work in the fields of navigation or target tracking.

Objectives

  • The student will receive a thorough understanding of linear, extended, unscented, and square root Kalman filters and their practical applications to real time strapdown navigation and target tracking. The student will also be exposed to Information filters, 2nd and 3rd order extended Kalman filters, particle filters, integrity monitoring, and methods of smoothing.
  • Emphasis is on practical applications, but sufficient supporting theory is provided to give attendees the necessary tools for meaningful research and development work in the field. Considerable time is devoted to modeling, the most difficult aspect of Kalman filtering, in an application setting.
  • There will be a high level of instructor/attendee interaction, designed to provide hands-on problem solving and solution discussions.

Prerequisites

  • A basic understanding of linear systems.
  • A basic understanding of probability, random variables, and stochastic processes.
  • A thorough familiarity with matrix algebra principles.

Who Should Attend?

  • Engineers who need a working knowledge of Kalman Filtering or who work in the fields of either navigation or target tracking.

Equipment You Should Bring

  • A laptop (PC or Mac) with full version of MATLAB 5.0 (or later) installed. This will allow you to work the problems in class and do the practice "homework" problems each evening. All of the problems will also be worked in class by the instructor, so this equipment is not required, but is recommended. These course notes are searchable and you can take electronic notes with the Adobe Acrobat 9 Reader we will provide you.

Materials You Will Keep

  • A color electronic copy of all course notes will be provided on a USB Drive or CD-ROM. Bringing a laptop to this class is highly recommended; power access will be provided.
  • A black and white hard copy of the course notes will also be provided.
  • Public Venue Attendees: Introduction to Random Signals and Applied Kalman Filtering, 3rd edition, by R. Grover Brown and Patrick Hwang, John Wiley & Sons, Inc., 1996. (Note: This arrangement does not apply to on-site contracts. Any books for on-site group contracts are negotiated on a case by case basis.)

Morning

Random Process Review

  • Random variables, probability densities, Gaussian and multivariate
  • Expectation, covariance matrix, random process, autocorrelation, power spectral density, stationary and nonstationary
  • Linear response, shaping filters

State Space Modeling

  • Models derived from differential equations, PSDs and block diagrams
  • Discrete time solution
  • Mean and covariance response
  • Markov and integrated Markov examples
  • Transition and process covariance

Random Process Simulation and Analysis

  • Vector random process simulation
  • Autocorrelation and PSD from data
  • Markov random process modeling and design
  • Computer demo

 

Afternoon

KF System Integration

  • Integration with complementary filtering
  • Integration examples
  • State space modeling
  • Simplified KF derivation

The Kalman Filter

  • Simplified algorithm description
  • Bias, random walk and Markov examples
  • Off-line error (covariance) analysis

Alternate Kalman Algorithms

  • State augmentation
  • Sequential processing
  • Known control inputs
  • Generalized KFs for correlated noises
  • LU decorrelation
  • Matrix partitioning for efficiency
Course: 122
Falls Church, VA

Learning the terms and how they play a role in GPS and how equipment processes GPS signals [was useful to my work]. The 2-day course discussed many of the terms I deal with in my job.

— Frank Crisafulli, USCG
Course: 557
Huntsville, AL

[My main objective was to] gain a basic understanding of navigation systems; this course exceeded this expectation with a lot of very in-depth information.

— Name withheld upon request, NASA
Course: 557
Huntsville, AL

I found everything to be useful. The review of filtering concepts was a great refresher and filled several holes in my knowledge. I’ve not done any GPS work before, so learning about how to integrate them into a navigation system was imminently practical.

— Name withheld upon request, NASA
Course: 557
Huntsville, AL

My primary objective was to gain an understanding of the physics behind inertial navigation systems as well as learn how to build a robust Kalman Filter and implement it. I did learn what I wanted to from this course.

— Name withheld upon request, NASA
Course: 557
Huntsville, AL

Understanding basic terminology is helpful for me just because I don’t work with Nav analysis daily. I’m about to start doing more on the Nav team and I think I have a good understanding of how to handle errors and not blindly use current Kalman Filter functions here.

— Name withheld upon request, NASA
Course: 557
Huntsville, AL

[My main objectives were to] increase new hires in our branch knowledge and awareness of Inertial Navigation and Kalman Filters. Goals were definitely met.

— Name withheld upon request, NASA
Course: 557
Huntsville, AL

I’ve been writing Kalman Filters for many different types of systems for many years. I was hoping to fill in some gaps in the mathmatical theory, and did.

— Name withheld upon request, NASA
Course: 557
Huntsville, AL

Dr. Pue kept in interesting. It’s easy to doze off in these type, but he kept it interesting.

— Name withheld upon request, NASA
Course: 557
Huntsville, AL

I’ve filled in the math behind the Kalman Filter which will help me understand some of the finer points.

— Name withheld upon request, NASA
Course: 557
Huntsville, AL

[The knowledge I acquired was] too much to list: IMU mechanism function, limitations, and considerations of navigation output from a Kalman filter, implementation strengths and weaknesses, when to correlate errors.

— Name withheld upon request, NASA
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